I don't have a clear idea of distinction between the two, to me the latter seems to be restatement of the former with added "procedure". completeness: every statement in the system can be either proved or disproved in the system; decidability: iff there exists an algorithm such that for every well-formed formula in that system there exists a maximum finite number N of steps such that the algorithm is capable of deciding in less than or equal to N algorithmic steps whether the formula is (semantically) valid or not valid; So a system can be complete and undecidable, right? If system is incomplete, does that necessarily mean that it is also undecidable? Could someone explain on a simple example? Thanks in advance.